The generalizations of NLSE based on underlying \({\cal {PT}}\) -symmetry[1]} may be broadly classified into three
different classes: (i) NLSE with \({\cal {PT}}\) -symmetric complex confining potential, (ii) the non-local NLSE,
and (iii) NLSE with LC and BLG terms. Solvable models of NLSE with \({\cal {PT}}\) -symmetric complex
localized potential[2]}, [3]}, [4]}, [5]}, [6]} have been considered which admits soliton solutions. The investigations on
\({\cal {PT}}\) -symmetry breaking as a function of the system parameters reveal a host of interesting issues including
the behaviour of solitons at the exceptional points[6]}. The non-local NLSE[8]}
is integrable and admits bright as well as dark soliton for the same range of the nonlinear strength.
The non-local vector NLSE is also integrable and amenable to exact solutions and real-valued physical
quantities[9]}. Further, it has lead to a new branch of integrable models
where non-local generalizations of previously known integrable models have been
considered[10]}, [11]}, [12]}.
